then the filter can be expressed as a polynomial finite sum of \(\mathbf {R}\) .
We call a graph filter linear "shift" invariant [1]} (LSI) all operator polynomial of \(\mathbf {R}\) . This notion of invariance with respect to a reference operator on graphs seems rather restrictive insofar as many reference operators on graphs do not systematically admit eigenspaces of dimension equal to 1 but eventually eigenspaces of dimension greater than 1. Thus, it will always be possible to construct a filter on graph which is a polynomial finite sum of a reference operator and therefore always invariant to its reference operator.
